A New Exceptional Family of Elements and Solvability of General Order Complementarity Problems

By using the concept of exceptional family, we propose a sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in Németh, 2010 (Theorem 3.1). Then we study some sufficient conditions for the nonexistence of exceptional family for GOCP in Hilbert space. Moreover, we prove that without exceptional family is a sufficient and necessary condition for the solvability of pseudomonotone general order complementarity problems

Multiferroic and Ferroic Topological Order in Ligand-Functionalized Germanene and Arsenene

Two-dimensional (2D) materials that exhibit ferroelectric, ferromagnetic, or topological order have been a major focal topic of nanomaterials research in recent years. The latest efforts in this field explore 2D quantum materials that host multiferroic or concurrent ferroic and topological order. We present a computational discovery of multiferroic state with coexisting ferroelectric and ferromagnetic order in recently synthesized CH2OCH3-functionalized germanene. We show that an electric-field-induced rotation of the ligand CH2OCH3 molecule can serve as the driving mechanism to switch the electric polarization of the ligand molecule, while unpassivated Ge p(z) orbits generate ferromagnetism. Our study also reveals coexisting ferroelectric and topological order in ligand-functionalized arsenene, which possesses a switchable electric polarization and a Dirac transport channel. These findings offer insights into the fundamental physics underlying these coexisting quantum orders and open avenues for achieving states of matter with multiferroic or ferroic-topological order in 2D-layered materials for innovative memory or logic device implementations

Smooth Flow in Diamond: Atomistic Ductility and Electronic Conductivity

Diamond is the quintessential superhard material widely known for its stiff and brittle nature and large electronic band gap. In stark contrast to these established benchmarks, our first-principles studies unveil surprising intrinsic structural ductility and electronic conductivity in diamond under coexisting large shear and compressive strains. These complex loading conditions impede brittle fracture modes and promote atomistic ductility, triggering rare smooth plastic flow in the normally rigid diamond crystal. This extraordinary structural change induces a concomitant band gap closure, enabling smooth charge flow in deformation created conducting channels. These startling soft-and-conducting modes reveal unprecedented fundamental characteristics of diamond, with profound implications for elucidating and predicting diamond’s anomalous behaviors at extreme conditions

The convergence of a one-step smoothing Newton method for P0-NCP based on a new smoothing NCP-function

AbstractThe nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the solution of a nonsmooth system of equations. By introducing a new smoothing NCP-function, the problem is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is proposed for solving the nonlinear complementarity problem with P0-function (P0-NCP) based on the new smoothing NCP-function. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. Without requiring strict complementarity assumption at the P0-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions

First-principles Study of High-Pressure Phase Stability and Superconductivity of Bi4I4

Bismuth iodide Bi4I4 exhibits intricate crystal structures and topological insulating states that are highly susceptible to influence by environments, making its physical properties highly tunable by external conditions. In this work, we study the evolution of structural and electronic properties of Bi4I4 at high pressure using an advanced structure search method in conjunction with first-principles calculations. Our results indicate that the most stable ambient-pressure monoclinic α−Bi4I4 phase in C2/m symmetry transforms to a trigonal P31c structure (ɛ−Bi4I4) at 8.4 GPa, then to a tetragonal P4/mmm structure (ζ−Bi4I4) above 16.6 GPa. In contrast to the semiconducting nature of ambient-pressure Bi4I4, the two high-pressure phases are metallic, in agreement with reported electrical measurements. The ɛ−Bi4I4 phase exhibits distinct ionic states of Iδ− and (Bi4I3)δ + (δ=0.4123 e), driven by a pressure-induced volume reduction. We show that both ɛ- and ζ−Bi4I4 are superconductors, and the emergence of pressure-induced superconductivity might be intimately linked to the underlying structural phase transitions

Investigation of the effect of thermal insulation materials on packaging performance

This investigation evaluates thermal insulation performance of a typical shipping container with different insulation materials. A mathematical model developed from our previous work was used to analyse the effect of packaging characteristics on insulative performance. A number of materials were employed as a liner to insulate a typical cardboard box and the effect of these materials on package insulative performance was evaluated through experimental tests and the transistent thermal model. The results showed that application of aluminium foil to the internal liner surface of polyethylene gave 46% increase in the package insulative performance compared to the original polyethylene insulated packages. An improvement of 79% and 106% in insulative performance per unit liner thickness was obtained from packages insulated with polyisocyanurate board and aerogel blanket compared to the polystyrene insulated package.The results also indicated that temperature surrounding the package played a significant role in the maximum insulation time. Furthermore, an excellent agreement was obtained between the mathematical model and the experimental results across all packaging aspects studied in this work

Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions

The iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair (X,Y) solutions of the generalized coupled Sylvester-conjugate matrix equations A1X+B1Y=D1X¯E1+F1, A2Y+B2X=D2Y¯E2+F2. On the condition that the coupled matrix equations are consistent, we show that the solution pair (X*,Y*) can be obtained within finite iterative steps in the absence of round-off error for any initial value given centrally symmetric (centrally antisymmetric) matrix. Moreover, by choosing appropriate initial value, we can get the least Frobenius norm solution for the new generalized coupled Sylvester-conjugate linear matrix equations. Finally, some numerical examples are given to illustrate that the proposed iterative method is quite efficient

The Inversion-Free Iterative Methods for Solving the Nonlinear Matrix Equation X

We present two inversion-free iterative methods for computing the maximal positive definite solution of the equation X+AHX-1A+BHX-1B=I. We prove that the sequences generated by the two iterative schemes are monotonically increasing and bounded above. We also present some numerical results to compare our proposed methods with some previously developed inversion-free techniques for solving the same matrix equation

Anisotropic Ripple Deformation in Phosphorene

Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.Comment: J. Phys. Chem. Lett. 201